We included **HMH Into Math Grade 5 Answer Key PDF** **Module 10 Lesson 2 Represent and Find the Size of Equal Parts **to make students experts in learning maths.

## HMH Into Math Grade 5 Module 10 Lesson 2 Answer Key Represent and Find the Size of Equal Parts

I Can divide a unit fraction by a whole number using a visual fraction model.

**Spark Your Learning**

A recreation center has a batting cage with a machine that pitches balls to the batter. Five friends sign up for a \(\frac{1}{2}\) hour of time in the batting cage. If they share the \(\frac{1}{2}\) hour equally, how much of a whole hour will each friend get in the batting cage? Explain.

Each friend will get ___________ hour in the batting cage.

Answer:

Each friend will get \(\frac{1}{10}\) hour in

the batting cage,

Explanation:

Given a recreation center has a batting cage with a

machine that pitches balls to the batter. Five friends sign up

for a \(\frac{1}{2}\) hour of time in the batting cage.

If they share the \(\frac{1}{2}\) hour equally,

So of a whole hour will each friend get in the batting cage is

\(\frac{1}{2 X 5}\) = \(\frac{1}{10}\) hour,

So each friend will get \(\frac{1}{10}\) hour in

the batting cage.

**Turn and Talk** How would your answer change if the friends had signed up for \(\frac{1}{4}\) hour?

Answer:

Each friend will get \(\frac{1}{20}\) hour in

the batting cage,

Explanation:

If the friends had signed up for \(\frac{1}{4}\) hour

then each friend will get \(\frac{1}{4 X 5}\) hour =

\(\frac{1}{20}\) hour.

**Build Understanding**

Question 1.

The distance around the track at the recreation center is \(\frac{1}{4}\) mile. Maeda, Will, and Holly plan to divide the distance evenly to practice sprints. What distance does each person run?

Write an expression and draw a visual model to represent the situation.

Answer:

\(\frac{1}{12}\) each person run,

Explanation:

Given the distance around the track at the recreation

center is \(\frac{1}{4}\) mile. Maeda, Will, and Holly

plan to divide the distance evenly to practice sprints.

The distance does each person run is \(\frac{1}{4 X 3}\) =

\(\frac{1}{12}\) mile.

A. What visual model did you use to represent the distance around the track? Explain.

Answer:

Used circle to represent the distance

around the track,

Explanation:

To represent the distance around the track I used circle,

divided it into as \(\frac{1}{12}\) mile as shown above.

B. How does your visual model show how the distance around the track was divided?

Answer:

1 as full part of the total circle divided in 12 equal parts,

Explanation:

My visual model full circle is been divided into

12 equal parts. The 12 parts around shows the

distance around the track.

C. How can you use your visual model to show the distance each person runs?

Answer:

The green part,

Explanation:

In the visual model the green part show the

distance each peson runs.

D. Use your visual model to write the division equation that models the situation.

Answer:

The division equation is \(\frac{1}{12}\),

Explanation:

By using the visual model the division equation

that models the situation is \(\frac{1}{12}\).

E. What distance does each person run?

Answer:

\(\frac{1}{12}\),

Explanation:

Each person runs \(\frac{1}{12}\).

**Step It Out**

Question 2.

One-third of the recreation center pool is reserved for lap swimming. If this part of the pool is divided equally for 2 swimmers, what fraction of the pool will each swimmer have?

A. Model the situation with an expression

Answer:

\(\frac{1}{3}\) X \(\frac{1}{2}\),

Explanation:

Given one-third of the recreation center pool is

reserved for lap swimming. If this part of the pool is

divided equally for 2 swimmers, the fraction of the pool

will each swimmer have with an expression is

\(\frac{1}{3}\) X \(\frac{1}{2}\).

B. Place a unit fraction strip under a 1-whole strip to show the dividend. Draw the model.

Answer:

Explanation:

Placed a unit fraction strip under a 1-whole strip to show the dividend

as \(\frac{1}{6}\).

C. Place fraction strips, all with the same denominator, that fit exactly under the unit fraction strip. Then draw the model.

Answer:

Explanation:

Placed fraction strips, all with the same denominator,

that fit exactly under the unit fraction strip.

Then drawn the model as shown above.

D. What fraction of the pool will each swimmer have? Write a division equation to model the situation.

Answer:

\(\frac{1}{6}\) of the pool will each swimmer have,

division equation is \(\frac{1}{6}\),

Explanation:

The fraction of \(\frac{1}{6}\) the pool will

each swimmer have, division equation is \(\frac{1}{6}\).

**Turn and Talk** Why do you need to use fraction strips with the same denominator to show how much of the pool each swimmer will have?

Answer:

They show equivalent fractions,

Explanation:

As fraction strips are used as a great way to illustrate

equivalent fractions so we use fraction strips with the

same denominator to show how much of the pool

each swimmer will have.

**Check Understanding**

Question 1.

One-fourth of a cheese wheel is divided equally among 5 people at a picnic. How much of a whoie wheel of cheese will each person get?

Answer:

\(\frac{1}{20}\),

Explanation:

Given one-fourth of a cheese wheel is divided

equally among 5 people at a picnic. So of a whole

wheel of cheese each person will get is

\(\frac{1}{4}\) X \(\frac{1}{5}\) = \(\frac{1}{20}\).

**Draw fraction strips to find the quotient.**

Question 2.

\(\frac{1}{6}\) ÷ 2 = ____________

Answer:

\(\frac{1}{12}\),

Explanation:

Given \(\frac{1}{6}\) ÷ 2 drawn the fraction strips and

found quotient as \(\frac{1}{6 X 2}\) = \(\frac{1}{12}\).

Question 3.

\(\frac{1}{2}\) ÷ 3 = ___________

Answer:

\(\frac{1}{6}\),

Explanation:

Given \(\frac{1}{2}\) ÷ 3 drawn the fraction strips and

found quotient as \(\frac{1}{2 X 3}\) = \(\frac{1}{6}\).

Question 4.

\(\frac{1}{3}\) ÷ 4 = _____________

Answer:

\(\frac{1}{12}\),

Explanation:

We use dividing by a whole number is the same as

multiplying by its reciprocal.

Given \(\frac{1}{3}\) ÷ 4 drawn the fraction strips and

found quotient as \(\frac{1}{3 X 4}\) = \(\frac{1}{12}\).

**On Your Own**

Question 5.

**Use Tools** A cement truck carries | ton of concrete. The truck will pour an equal amount of concrete for each of two houses.

Draw a visual model to represent the problem.

Answer:

Explanation:

Given 1 cement truck carries 1 ton of concrete.

The truck will pour an equal amount of concrete

for each of two houses. Drawn a visual model to

represent the problem as shown above.

Write a division equation to model this situation.

Answer:

\(\frac{1}{2}\),

Explanation:

A division equation to model this situation is

\(\frac{1}{2}\).

Explain what the quotient means in this situation.

Answer:

Quotient means 0.5 tons each house,

Explanation:

Here the quotient means in this situation means

0.5 tons for each house.

**Divide. Use a visual model to find the quotient.**

Question 6.

\(\frac{1}{3}\) ÷ 3 = ___________

Answer:

\(\frac{1}{9}\),

Explanation:

We use dividing by a whole number is the same as

multiplying by its reciprocal.

The quotient of \(\frac{1}{3}\) ÷ 3 =\(\frac{1}{3}\) X \(\frac{1}{3}\) = \(\frac{1}{3 X 3}\) = \(\frac{1}{9}\).

Question 7.

_________ = \(\frac{1}{8}\) ÷ 2

Answer:

\(\frac{1}{16}\),

Explanation:

We use dividing by a whole number is the same as

multiplying by its reciprocal.

The quotient of \(\frac{1}{8}\) ÷ 2 = \(\frac{1}{8}\) X \(\frac{1}{2}\) = \(\frac{1}{8 X 2}\) = \(\frac{1}{16}\).

Question 8.

__________ = \(\frac{1}{5}\) ÷ 4

Answer:

\(\frac{1}{20}\),

Explanation:

We use dividing by a whole number is the same as

multiplying by its reciprocal.

The quotient of \(\frac{1}{5}\) ÷ 4 = \(\frac{1}{5}\) X \(\frac{1}{4}\) = \(\frac{1}{5 X 4}\) = \(\frac{1}{20}\).

Question 9.

\(\frac{1}{4}\) ÷ 4 = __________

Answer:

\(\frac{1}{16}\),

Explanation:

We use dividing by a whole number is the same as

multiplying by its reciprocal.

The quotient of \(\frac{1}{4}\) ÷ 4 = \(\frac{1}{4}\) X \(\frac{1}{4}\) = \(\frac{1}{4 X 4}\) = \(\frac{1}{16}\).

Question 10.

_________ = \(\frac{1}{6}\) ÷ 3

Answer:

\(\frac{1}{18}\),

Explanation:

We use dividing by a whole number is the same as

multiplying by its reciprocal.

The quotient of \(\frac{1}{6}\) ÷ 3 = \(\frac{1}{6}\) X \(\frac{1}{3}\) = \(\frac{1}{6 X 3}\) = \(\frac{1}{18}\).

Question 11.

\(\frac{1}{10}\) ÷ 2 = ___________

Answer:

\(\frac{1}{20}\),

Explanation:

We use dividing by a whole number is the same as

multiplying by its reciprocal.

The quotient of \(\frac{1}{10}\) ÷ 2 = \(\frac{1}{10}\) X \(\frac{1}{2}\) = \(\frac{1}{10 X 2}\) = \(\frac{1}{20}\).

Question 12.

**Use Structure** Gerardo divides \(\frac{1}{2}\) by 2, and then divides the quotient by 2 again. Draw a circle to represent one whole. Then use it to explain how Gerardo’s work is similar to dividing \(\frac{1}{2}\) by 4.

Answer:

Explanation:

Given Gerardo divides \(\frac{1}{2}\) by 2 and

then divides the quotient by 2 again. So first \(\frac{1}{2}\) ÷ 2 =

\(\frac{1}{2 X 2}\) = \(\frac{1}{4}\) again by 2

\(\frac{1}{4}\) ÷ 2 = \(\frac{1}{4 X 2}\) = \(\frac{1}{8}\).

Drawn a circle to represent one whole as shown above,

instead of twice dividing Gerardo divided directly \(\frac{1}{2}\) by 4 as

\(\frac{1}{2 X 4}\) = \(\frac{1}{8}\).

**I’m in a Learning Mindset!**

How do I stay focused when dividing unit fractions by whole numbers?

Answer:

Keep first part same, switch or change operation and

flip the whole number,

Explanation:

When dividing unit fractions by whole numbers we should keep

first part switch or change operation and flip the whole number,

for example in unit fraction numerator will be always 1 we take

\(\frac{1}{5}\) ÷ 2 here we keep \(\frac{1}{5}\),

we change operator division ÷ to multiplication and flip the

whole number 2 as reciprocal \(\frac{1}{2}\), So now

we calculate \(\frac{1}{5}\) ÷ 2 as

\(\frac{1}{5}\) X \(\frac{1}{2}\) = \(\frac{1}{5 X 2}\) =

\(\frac{1}{10}\).